Hello I am working on an accounting problem using reciprocal method of allocation which is basically a matrix algebra. However, I cannot seem to solve the following.

Please advise. I need to find what X, Y, and Z equal to.

X Y Z
X .2 .1 .2
Y .4 .1
Z .0909

COST
X 100,000
Y 50,000
Z 40,000

So I am assuming the first function is: X=100,000 + .2X + .4Y
I am not sure if this is correct. Should it be X=100,000 + .4Y